CPM Homework Help : APCALC Problem 11-95

Calculate the arc length of the parametric curve given by $x(t) = t^2 - t$ and $y(t) =\frac { 1 } { 3 }t^3 − t$ over $0 ≤ t ≤ 1$ .

Step 1:

$\int_0^1\sqrt{(x^\prime(t))^2+(y^\prime(t))^2}dt$

Step 2:

$\int_0^1\sqrt{(2t-1)^2+(t^2-1)^2}dt$

Use a calculator to evaluate this integral.